Hi potiche,
Just going by what you have said, the presence of aquatic moss and lack of grass, indicates to me to be very poor drainage and possibly but not necessarily over-shading.
So, I would have the drainage looked at firstly, otherwise the problem may reoccur time after time.
Grass having a yellowish appearance in winter, especially in an exposed coastal location would seen fairly normal, but this can be adjusted with the application of an autumn feed of the appropriate fertilizer.
Personally, I don't think anything compares with grass for a good lawn and I wouldn't use anything else, unless it was a difficult area to maintain like a steep bank.